Titlebook: Interfaces: Modeling, Analysis, Numerics; Eberhard Bänsch,Klaus Deckelnick,Paola Pozzi Textbook 2023 The Editor(s) (if applicable) and The

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Some Notions from Differential Geometry, manifolds, we study surfaces evolving in time. In particular, we introduce the definitions of material derivative and normal time derivative, and derive useful versions of transport theorems that will be frequently used in subsequent chapters.

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Numerical Methods for Complex Interface Evolutions,acking, are discussed and compared. Then, the application of mesh moving as the most straightforward representative of interface tracking as well as the level-set method as a prominent example of interface capturing to the numerical approximation of two phase flows are detailed.

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Exercises,In this chapter exercises for the material presented in the book are given.

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